Spatiotemporal approach for time-varying global image motionestimation

Image motion estimation using the spatiotemporal approach has largely relied on the constant velocity assumption, and thus becomes inappropriate when the velocity of the imaged scene or the camera changes during the data acquisition time. Using a polynomial or a trigonometric polynomial model for the time variation of the image motion, spatiotemporal algorithms are developed in this paper to handle time-varying (but space-invariant) motion. Under these models, it is shown that time-varying image motion estimation is equivalent to parameter estimation of one-dimensional (1-D) polynomial phase or phase-modulated signals, which allows one to exploit well-established results in radar signal processing. When compared with alternative approaches, the resulting motion estimation algorithms produce more accurate estimates. Simulation results are provided to demonstrate the proposed schemes.     

Singularity Detection of Signals Based on their Wavelet Transform

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A new time delay estimation in subbands for resolving multiplespecular reflections

A new time delay estimation procedure is proposed using the multiresolution analysis framework through a discrete wavelet transform (DWT). Once the signals are decomposed, the time delays are estimated iteratively in each subband using two different adaptation mechanisms that minimize the mean squared error (MSE) between the reference and primary signals in the corresponding subband and level. The localization of the minima of the MSE curves at different levels and subbands is used in order to arrive at the time delay estimates. The proposed scheme is then applied to a real-life problem of underwater target detection from acoustic backscattered data     

On sampling theorem, wavelets, and wavelet transforms

The classical Shannon sampling theorem has resulted in many applications and generalizations. From a multiresolution point of view, it provides the sine scaling function. In this case, for a band-limited signal, its wavelet series transform (WST) coefficients below a certain resolution level can be exactly obtained from the samples with a sampling rate higher than the Nyquist rate. The authors study the properties of cardinal orthogonal scaling functions (COSF), which provide the standard sampling theorem in multiresolution spaces with scaling functions as interpolants. They show that COSF with compact support have and only have one possibility which is the Haar pulse. They present a family of COSF with exponential decay, which are generalizations of the Haar function. With these COSF, an application is the computation of WST coefficients of a signal by the Mallat (1989) algorithm. They present some numerical comparisons for different scaling functions to illustrate the advantage of COSF. For signals which are not in multiresolution spaces, they estimate the aliasing error in the sampling theorem by using uniform samples     

Generalized Daubechies Wavelet Families

We present a generalization of the orthonormal Daubechies wavelets and of their related biorthogonal flavors (Cohen-Daubechies-Feauveau, 9/7). Our fundamental constraint is that the scaling functions should reproduce a predefined set of exponential polynomials. This allows one to tune the corresponding wavelet transform to a specific class of signals, thereby ensuring good approximation and sparsity properties. The main difference with the classical construction of Daubechies is that the multiresolution spaces are derived from scale-dependent generating functions. However, from an algorithmic standpoint, Mallat's fast wavelet transform algorithm can still be applied; the only adaptation consists in using scale-dependent filter banks. Finite support ensures the same computational efficiency as in the classical case. We characterize the scaling and wavelet filters, construct them and show several examples of the associated functions. We prove that these functions are square-integrable and that they converge to their classical counterparts of the corresponding order.     

Improving Automatic Detection of Defects in Castings by Applying Wavelet Technique

X-ray-based inspection systems are a well-accepted technique for identification and evaluation of internal defects in castings, such as cracks, porosities, and foreign inclusions. In this paper, some images showing typical internal defects in the castings derived from an X-ray inspection system are processed by some traditional methods and wavelet technique in order to facilitate automatic detection of these internal defects. An X-ray inspection system used to detect the internal defects of castings and the typical internal casting defects is first addressed. Second, the second-order derivative and morphology operations, the row-by-row adaptive thresholding, and the two-dimensional (2-D) wavelet transform methods are described as potentially useful processing techniques. The first method can effectively detect air-holes and foreign-inclusion defects, and the second one can be suitable for detecting shrinkage cavities. Wavelet techniques, however, can effectively detect the three typical defects with a selected wavelet base and multiresolution levels. Results indicate that 2-D wavelet transform is a powerful method to analyze images derived from X-ray inspection for automatically detecting typical internal defects in the casting     

Multiresolution FIR neural-network-based learning algorithm applied to network traffic prediction

In this paper, a multiresolution finite-impulse-response (FIR) neural-network-based learning algorithm using the maximal overlap discrete wavelet transform (MODWT) is proposed. The multiresolution learning algorithm employs the analysis framework of wavelet theory, which decomposes a signal into wavelet coefficients and scaling coefficients. The translation-invariant property of the MODWT allows alignment of events in a multiresolution analysis with respect to the original time series and, therefore, preserving the integrity of some transient events. A learning algorithm is also derived for adapting the gain of the activation functions at each level of resolution. The proposed multiresolution FIR neural-network-based learning algorithm is applied to network traffic prediction (real-world aggregate Ethernet traffic data) with comparable results. These results indicate that the generalization ability of the FIR neural network is improved by the proposed multiresolution learning algorithm.     

The time–frequency analysis approach of electric noise based on the wavelet transform

In this paper, the wavelet transform approach has been firstly introduced to analyze electric noise in a transistor. Due to the multiresolution ability of wavelet transform, we can separate noise signal into several detail signals and approximation signal which can be interpreted in terms of the noise output of a generalized constant-Q filter bank and low pass filter, respectively.Based on this approach, the fractal and chaos characteristic of 1/f noise are obtained, the smaller burst noise pulse embedded in the white noise and 1/f noise can be detected, and the noise spectrum can also be calculated from short noise data. These results demonstrate that wavelet transform approach is a useful tool for investigation of noise mechanism of a transistor.     

High-order balanced multiwavelets: theory, factorization, anddesign

This paper deals with multiwavelets and the different properties of approximation and smoothness associated with them. In particular, we focus on the important issue of the preservation of discrete-time polynomial signals by multifilterbanks. We introduce and detail the property of balancing for higher degree discrete-time polynomial signals and link it to a very natural factorization of the refinement mask of the lowpass synthesis multifilter. This factorization turns out to be the counterpart for multiwavelets of the well-known zeros at π condition in the usual (scalar) wavelet framework. The property of balancing also proves to be central to the different issues of the preservation of smooth signals by multifilterbanks, the approximation power of finitely generated multiresolution analyses, and the smoothness of the multiscaling functions and multiwavelets. Using these new results, we describe the construction of a family of orthogonal multiwavelets with symmetries and compact support that is indexed by increasing order of balancing. In addition, we also detail, for any given balancing order, the orthogonal multiwavelets with minimum-length multifilters     

Family of scaling chirp functions, diffraction, and holography

It is observed that diffraction is a convolution operation with a chirp kernel whose argument is scaled. Family of functions obtained from a prototype by shifting and argument scaling form the essential ground for wavelet framework. Therefore, a connection between diffraction and wavelet transform is developed. However, wavelet transform is essentially prescribed for time-frequency and/or multiresolution analysis which is irrelevant in our case. Instead, the proposed framework is useful in various location-depth type of analysis in imaging. The linear transform when the analyzing functions are the chirps is called the scaling chirp transform. The scaled chirp functions do not satisfy the commonly used admissibility condition for wavelets. However, it is formally shown that these neither band nor time limited signals can be used as wavelet functions and the inversion is still possible. Diffraction and in-line holography are revisited within the scaling chirp transform context. It is formally proven that a volume in-line hologram gives perfect reconstruction. The developed framework for wave propagation based phenomena has the potential of advancing both signal processing and optical applications     

On Translation Invariant Subspaces and Critically Sampled Wavelet Transforms

The discrete wavelet transform (DWT) is attractive for many reasons. Its sparse sampling grid eliminates redundancy and is very efficient. Its localized basis functions are well suited for processing non–stationary signals such as transients. On the other hand, its lack of translation invariance is a major pitfall for applications such as radar and sonar, particularly in a multipath environment where numerous signal components arrive with arbitrary delays. The paper proposes the use of robust representations as a solution to the translation invariance problem. We measure robustness in terms of a mean square error for which we derive an expression that describes this translation error in the Zak domain. We develop an iterative algorithm in the Zak domain for designing increasingly robust representations. The result is an approach for generating multiresolution subspaces that retain most of their coefficient energy as the input signal is shifted. A typical robust subspace retains 98% of its energy, a significant improvement over more traditional wavelet representations.     

激光干涉测速中的小波快速算法研究

为了提高小波变换在激光干涉测速中的计算速度,分析了小波变换的计算过程,提出了两种快速算法,通过分析对比,选择了一种适合于全光纤位移干涉信号的算法,在相同条件下,对同一信号分别采用常规小波变换和使用快速傅里叶变换的快速方法进行处理。结果表明,采用快速算法的小波变换对信号的处理能力并没有下降,且提高了小波变换的运算效率。这种快速算法用于瞬态位移干涉仪信号处理是行之有效的,可以提高数据处理的速度,有利于小波变换在工程中的应用。     

Multiple scale correlation of signals by shift-invariant discrete wavelet transform

Correlation of signals at multiple scales of observation is useful for multiresolution interpretation of image, data and target signature analysis. Multiresolution analysis is inherent in the discrete wavelet transform (DWT), but shift-variance of the coefficients of the transform in dyadic orthogonal and biorthogonal basis spaces is the problem associated with it. Shift-variance of the transform and absence of a direct transform domain relationship make correlation of signals by the DWT inconvenient at multiple scales. The circulant shift property of the DWT coefficients is used in a novel way to produce correlation of signals at multiple scales with the critically sampled DWT only. The algorithm is derived in both discrete time and z-domain for signal vectors of finite duration. The algorithm is independent of signal waveform and wavelet kernel and is applied particularly for multiple scale correlation of radar signals, namely linear frequency modulated (LFM) chirp signals.     

PAPR Reduction in OFDM Systems: Polynomial-Based Compressing and Iterative Expanding

In this paper a companding-based scheme is proposed to reduce the Peak-to-average power ratio (PAPR) of an orthogonal frequency division multiplexing system. At the transmitter side, a compressing polynomial function is appended to the inverse discrete Fourier transform block; and at the receiver the transmitted signal is retrieved iteratively through combining the discrete Fourier transform block with a reverse expanding function. In the iterative algorithm the Jacobi’s method is used for solving the equations. Also, the general form of the compressing polynomial functions is attained through the use of Daubechies wavelet functions. As an advantage, the proposed method involves less complexity at the transmitter compared to other PAPR reduction methods. Furthermore, it requires less increasing to signal-to-noise ratio for the same bit error rate in comparison with other companding methods. The order of compressing polynomial and the number of iterations for the proposed algorithm at the receiver can be set in accordance with the performance-complexity trade off.     

M带小波变换在图象中的应用

小波变换是近年来兴起的一种时频域信号分析理论,是信号分析处理的一种强有力的新工具.本文根据小波变换的特点,在Mallat二带多分辨分析的基础上,讨论分析了信号的多带多分辨分析的理论和实现算法,并将这一理论和算法应用于图象处理,取得了满意效果.     

Progressive wavelet correlation using Fourier methods

This paper derives a multiresolution analysis technique for performing correlations on wavelet representations of images. The technique maps the images into the wavelet-frequency domain to take advantage of high-speed correlation in the frequency domain. It builds on Vaidyanathan's (1993) wavelet correlation theorem, which shows that subsamples of correlations of two signals can be obtained from a sum of correlations of subbands of wavelet representations of those signals. Our algorithm produces the correlations at lowest resolution by applying the convolution theorem to subband correlations. A new multiresolution technique fills in the missing correlation data by incrementally inverting the wavelet transform and refining the Fourier transform. When applied to JPEG representations of data, the lowest resolution correlations can he performed directly on the JPEG images to produce 1/64th of the correlation points. Each of three incremental steps quadruple the number of correlation points, and the process can be halted at any point if the intermediate results indicate that the correlation will not find a match     

Two-band wavelets and filterbanks over finite fields with connections to error control coding

Recently, we have developed a new framework to study error-control coding using finite-field wavelets and filterbanks (FBs). This framework reveals a rich set of signal processing techniques that can be exploited to investigate new error correcting codes and to simplify encoding and decoding techniques for some existing ones. The paper introduces the theory of wavelet decompositions of signals in vector spaces defined over Galois fields. To avoid the limitations of the number theoretic Fourier transform, our wavelet transform relies on a basis decomposition in the time rather than the frequency domain. First, by employing a symmetric, nondegenerate canonical bilinear form, we obtain a necessary and sufficient condition that the basis functions defined over finite fields must satisfy in order to construct an orthogonal wavelet transform. Then, we present a design methodology to generate the mother wavelet and scaling function over finite fields by relating the wavelet transform to two-channel paraunitary (PU) FBs. Finally, we describe the application of this transform to the construction of error correcting codes. In particular, we give examples of double circulant codes that are generated by wavelets.     

Estimation of fractal signals using wavelets and filter banks

A filter bank design based on orthonormal wavelets and equipped with a multiscale Wiener filter was recently proposed for signal restoration and for signal smoothing of 1/f family of fractal signals corrupted by external noise. The conclusions obtained in these papers are based on the following simplificative hypotheses: (1) The wavelet transformation is a whitening filter, and (2) the approximation term of the wavelet expansion can be avoided when the number of octaves in the multiresolution analysis is large enough. In this paper, we show that the estimation of 1/f processes in noise can be improved avoiding these two hypotheses. Explicit expressions of the mean-square error are given, and numerical comparisons with previous results are shown     

Multiresolution wavelet analysis of evoked potentials

Neurological injury, such as from cerebral hypoxia, appears to cause complex changes in the shape of evoked potential (EP) signals. To characterize such changes we analyze EP signals with the aid of scaling functions called wavelets. In particular, we consider multiresolution wavelets that are a family of orthonormal functions. In the time domain, the multiresolution wavelets analyze EP signals at coarse or successively greater levels of temporal detail. In the frequency domain, the multiresolution wavelets resolve the EP signal into independent spectral bands. In an experimental demonstration of the method, somatosensory EP signals recorded during cerebral hypoxia in anesthetized cats are analyzed. Results obtained by multiresolution wavelet analysis are compared with conventional time-domain analysis and Fourier series expansions of the same signals. Multiresolution wavelet analysis appears to be a different, sensitive way to analyze EP signal features and to follow the EP signal trends in neurologic injury. Two characteristics appear to be of diagnostic value: the detail component of the MRW displays an early and a more rapid decline in response to hypoxic injury while the coarse component displays an earlier recovery upon reoxygenation     

一种新的二维非线性提升小波变换方法

根据图像的统计信息,本文构造了一种新的非线性算子即统计算子,提出了基于该算子的一种新的非线性提升小波分析方法.使图像经过该方法变换以后,在无量化失真的前提下,以较大概率取得零高频系数.本文将该方法与现存文献中所提出的非线性形态学小波等分析方法,进行了标准图像的测试分析,实验结果显示,利用本文所提出的基于统计算子的提升小波分析的方法所得到的高频子带的熵都低于其它几种非线性小波变换,取得了很好的分析结果.